The purpose of this article is to study and investigate statistically probability convergence for the sequence of random variables by virtue of deferred N\“{o}rlund and deferred Euler summability mean. With the aid of MATLAB software, we also graphically exhibits the statistically probability convergence for probability density function of random variables. Further, as an application of our newly form summability mean, we prove Korovkin type approximation theorem via deferred N\”{o}rlund and deferred Euler statistically probability convergence and present compelling instances to illustrate the findings.